One well-known technique of seismic prospecting involves the placement of a linear array of geophones along the surface of the earth, or a body of water, producing a "shot", or source of seismic signals, through the use of an explosive charge or vibratory stimulus, and receiving signals reflected from the subsurface formations, or seismic "events", at each of the geophones in the linear array. The locations of the geophones and the signal source are then moved, in a well known manner, and the process is repeated. In this way, raw data in the form of a plurality of "common shot gathers" are collected along a seismic line of interest.
To analyze the raw data the data is gain-adjusted in a well-known manner to remove the influence of distance between various source and receiver pairs, and deconvolved to produce a relatively narrow pulse in response to each seismic event. The geometry of the common shot gathers is also converted in a well-known way to a plurality of "common midpoint gathers", one of which is illustrated in FIG. 1. The common midpoint gather is defined as those source and receiver pairs which have a common midpoint. In FIG. 1, S.sub.i denotes the source location, R.sub.i denotes the associated receiver location, x is the source-receiver offset, equal to R.sub.i -S.sub.i, and the common midpoint value is defined as (R.sub.i +S.sub.i)/2. The formula relating travel time of the seismic signal from the source S.sub.i (x) to the receiver R.sub.i (x) is given by v.sup.2 t.sup.2 (x)=x.sup.2 +4d.sup.2, where v is velocity of propagation, t is travel time, and d is the distance from zero offset (x=0) to the seismic reflection. By defining 2d=vt(0), t(0) being the travel time of a signal from source S.sub. 0 to colocated receiver R.sub.0, the following formula results: EQU v.sup.2 t.sup.2 (x)=x.sup.2 +v.sup.2 t.sup.2 (0).
This formula, which defines the normal moveout relationship, is the most commonly used method of determining the signal arrival time differences of seismic data as a function of the offset distance of receiver from the source. The normal moveout relationship is hyperbolic between offset x and time t(x).
It is well known in the art that common midpoint data are noisy to the point where t(x) cannot be measured directly, and in order to reveal the unknown velocity v, corresponding to a particular event, a velocity analysis must be undertaken. Furthermore, since the velocity varies with both depth d, and position x, many such velocity analyses must be performed along the seismic line of interest to establish these variations. Clearly, the amount of time required to perform each analysis will greatly impact the time required to analyze an entire line.
Heretofore, each velocity analysis has been performed in accordance with a technique such as that proposed by Tanner and Koehler, in "Velocity Spectra-Digital Computer Derivation and Applications of Velocity Functions", Geophysics, v. 34, pp. 859-899 (1969), as follows: A set of trial velocities are used to "stack" the data, and then either a manual or automatic search is made to determine that velocity which gives the best response to a particular event. This is explained with reference to FIGS. 2-4. FIG. 2 illustrates common midpoint seismic data, which for the purposes of simplicity of explanation, is a noise-free single event, shown as a function of offset x and time t. In FIG. 2, the seismic "wavelet" corresponding to the event is shown as having a normal hyperbolic moveout relationship as defined above. The prior art method of velocity analysis is to "correct" the data with a suite of velocities, "stack" the data for each such velocity, and examine the result of the stacked data, choosing the velocity that results in the stack of highest amplitude. The assumption is that the highest amplitude is produced by the closest velocity.
With reference to FIGS. 3A and 3B, a first trail velocity is chosen and the data is corrected, i.e. the effect of the normal moveout relationship is removed, making each recording at the various shotreceiver offsets look like they were recorded at x=0. This is done by shifting the collection of seismic wavelets up in time using the normal moveout relationship and the estimated trial velocity, as graphically illustrated in FIG. 3A. The shifted wavelets are then summed along offset x to produce summed trace or stack 2, FIG. 3B.
FIG. 4 shows the shifted common midpoint data using a more correct estimate of velocity, resulting in a stack 4 having a higher amplitude.
Having determined the velocity, for a particular event, within a reasonable tolerance, the stack of the common midpoint gather, or "zero offset trace" is used to portray the associated seismic event in pictorial form, an example of which will be referred to below. The stacked data is so used since the individual reflection signals are usually too noisy to accurately portray useful information. By stacking the common midpoint gathers using a good velocity estimate, the step of summing greatly enhances the information, by increasing the signal-to-noise ratio. The closer the velocity used to stack the data is to the actual velocity, the better the enhancement of the information will be.
It will be appreciated that the traditional processing technique described above requires that each set of common midpoint data be stacked using a relatively large number of trial velocities depending upon the required tolerance in the velocity estimate, and any a priori knowledge of the propagation velocity at nearby or similar formations. Moreover, it will be appreciated that the stack is not performed using the exact (within tolerance) velocity required, but is rather based on an interpolation using the suite of trial velocities.